Right, then why aren't we taught that we don't know why electrons react the way they do from early on? As I've mentioned above, cutting out the complicated details would provide students with a much more comprehensible overview.
I was taught that. I don't even know where I picked it up. My impression is that physicists are pretty upfront about it. "Shut up and calculate!" and all that, eh?
> cutting out the complicated details would provide students with a much more comprehensible overview.
I'm not sure I know what you mean. The details are complicated, the essence is comprehensible.
F = ma
E = mc²
I accept that the physics curricula in different places will likely put a different emphasis on this so others will have a different experience. My problem is that I feel deprived that I wasn't made aware of these issues until much later.
Leaving out the intermediary levels isn't a loss if one is only painting the scope or overview to students. You mention 'the question of why is the domain of philosophers and theologians', well it so happens that I first learned about these issues not in physics but rather in HPS - History and Philosophy of Science - which was an adjunct subject to physics and chemistry. The trouble was that I studied HPS pretty late in the picture so to speak.
Anyway, as I see it, it wouldn't hurt to add a little HPS to the high school science curriculum. There was essentially none of that at my school except for mention of the usual suspects - Dalton, Faraday, Volta, etc. Unfortunately we were given no information about the background surrounding their scientific discoveries - that contextual stuff such as the state of science, the zeitgeist in which the discoverers lived and such. Having knowledge of the scope and extent of science at any point in history enables one to imagine oneself in the mind of the scientist of that time, what his obstacles were, the extent of his scientific knowledge at the time of discovery, etc.
Looking at scientists and their work in some detail gives us a better understanding of the state of the art of science at the time and it's surprising how useful this turns out to be. One suddenly understands how a contemporary working in isolation on one side of the planet can come up with the same or very similar idea as another who's on the other side of the planet and do almost at the same instant. This has happened so often throughout history it seems almost uncanny. A classic instance of this is Josiah Willard Gibbs and his work on laws of thermodynamics.
Another similar case is Kekulé's brilliant work in the 1860s where he realised that carbon atoms took on a hexagonal shape in the benzene ring. His insight came just at the ideal time when a confluence of ideas made organic chemistry take off and never look back. Similarly with technology, Young's famous (or should that be 'infamous') double slit experiament informs us of the state of optics and optical engineering in the early 19th Century.
Back to physics: there are many other examples of complex ideas in physics that can be explained simply to beginners that put the subject into perspective. One is Planck and the Ultraviolet Catastrophe that led to his now-famous constant which then led to Planck length, Planck time etc.
If you just chalked the constant up on the board without futher explanation then its importance would likely have not sunk in - anyway not at first. But if you also mentioned this remarkably small constant also explains why it's not possible to make an oscillator with an infinite number of steps in frequency (i.e. infinitely variable) then add the rider that it follows that it's impossible to make a clock whose second is infinitely divisible because physics says 'hey no, I won't let you do that' then students will never forget the constant's importance.
Why such simplifted explanations are important I can illustrate from my own experience, I was taught E=hv and was using the relationship long before I understood what h represented. In my experience, teaching physics by rote is very counterproductive. It's why in my eyes Bohr gets deducted points for his 'shutup-and-calculate' philosophy. I often wonder how many people have been turned off physics by tedious procedural stuff sans adequate explanation.
You mention two famous formulae so let's use them as examples. Also, you've written them up in their simplest forms and there's nothing wrong with that, as that's the way almost every student will first encounter them. Let's start Newton: when or after teaching his Laws of Motion you should also mention that Einstein built on them with Relativity. They'll almost certainly know this already so it doesn't contribute much but if you then add that Einstein couldn't have come up Relativity, especially so General Relativity, without the help of several extremely brilliant people† who lived in the intervening years between him and Newton (here, the time line is important so as to put things into proper perspective).
Explain that Lagrange reformulated Newtonian Mechanics so that it could be understood from a quite different perspective and that later it was further developed by Hamilton and thus Lagrangian and Hamiltonian Mechanics were born and that both were crucial to the development of Quantum Mechanics and Relatively - but at this juncture it isn't necessary or desirable to teach their underlying theory as it would only confuse.
Similarly, when putting this in context with their existing (popular culture level) knowledge of the Quantum Mechanics you could perhaps mention that Rowan Hamilton's reformulation of Lagrangian Mechanics saw the introduction of what's known as the Hamiltonian operator which describes the total energy of the system. Even if they don't remember anything else at this stage then it's important for them never to forget the word Hamiltonian as they'll see much, much more of it in the future.
By now, you're likely thinking I've ground the point overly fine and no doubt that's true but let me just say this: none of this overview perspective of physics was taught to me in my early training, moreover, I know of others who also were never given this background.
Incidentally, to drive the point home let me give you an example. During my time at university an examiner included a simple 'wakeup' type question in a third year physics examination that flummoxed many students. No, I wasn't in that year or I'd likely have been flummoxed too. The question without any additional explanation was just:
Derive the expression F=ma
The required answer was:
2nd Law: Force is proportional to time rate change of momentum, thus:
F ∝ (mv - mu)/t
(v-u)/t = a
Proportionality constant k = 1
F ∝ kma
∴ F = ma
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† And others, Ricci-Curbastro, Lorentz, Minkowsky, etc.